Can't find the Shader/UVs tab
Curves object's type doesn't have that panel

That panel is available only for Mesh type objects like the cube or the cylinder. Unrwapping is an operation related to faces, polygons, which in the filled and extruded curves are generated "on the fly" and not directly accessible.

Curves are an object type on their own, so you'll need to convert the curve to mesh in order to access those operators.